Evaluation of singlet oxygen explicit dosimetry for predicting ... · Keywords: photodynamic therapy; singlet oxygen explicit dosimetry, explicit dosimetry; singlet oxygen; photodynamic

Evaluation of singlet oxygen explicitdosimetry for predicting treatmentoutcomes of benzoporphyrinderivative monoacid ring A-mediatedphotodynamic therapy

Michele M. KimRozhin PenjweiniTimothy C. Zhu

Michele M. Kim, Rozhin Penjweini, Timothy C. Zhu, “Evaluation of singlet oxygen explicit dosimetry forpredicting treatment outcomes of benzoporphyrin derivative monoacid ring A-mediatedphotodynamic therapy,” J. Biomed. Opt. 22(2), 028002 (2017), doi: 10.1117/1.JBO.22.2.028002.

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Evaluation of singlet oxygen explicit dosimetry forpredicting treatment outcomes of benzoporphyrinderivative monoacid ring A-mediated photodynamictherapy

Michele M. Kim,a,b Rozhin Penjweini,a and Timothy C. Zhua,*aUniversity of Pennsylvania, Department of Radiation Oncology, Philadelphia, Pennsylvania, United StatesbUniversity of Pennsylvania, Department of Physics and Astronomy, Philadelphia, Pennsylvania, United States

Abstract. Existing dosimetric quantities do not fully account for the dynamic interactions between the key com-ponents of photodynamic therapy (PDT) or the varying PDT oxygen consumption rates for different fluence rates.Using a macroscopic model, reacted singlet oxygen (½1O2�rx) was calculated and evaluated for its effectivenessas a dosimetric metric for PDT outcome. Mice bearing radiation-induced fibrosarcoma tumors were treated withbenzoporphyrin derivative monoacid ring A (BPD) at a drug-light interval of 3 h with various in-air fluences (30 to350 J∕cm2) and in-air fluence rates (50 to 150 mW∕cm2). Explicit measurements of BPD concentration andtissue optical properties were performed and used to calculate ½1O2�rx, photobleaching ratio, and PDT dose.For four mice, in situ measurements of 3O2 and BPD concentration were monitored in real time and used tovalidate the in-vivo photochemical parameters. Changes in tumor volume following treatment were used to deter-mine the cure index, CI ¼ 1 − k∕kctr, where k and k ctr are the tumor regrowth rates with PDT and without PDT,respectively. The correlation between CI and the dose metrics showed that the calculated ½1O2�rx at 3 mm isan effective dosimetric quantity for predicting treatment outcome and a clinically relevant tumor regrowth end-point. © 2017 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.JBO.22.2.028002]

Keywords: photodynamic therapy; singlet oxygen explicit dosimetry, explicit dosimetry; singlet oxygen; photodynamic therapy dose;benzoporphyrin derivative monoacid ring A; in-vivo mouse study.

Paper 160855R received Dec. 16, 2016; accepted for publication Jan. 24, 2017; published online Feb. 10, 2017.

1 IntroductionAs a nonionizing radiation treatment, photodynamic therapy(PDT) has been used effectively for the treatment of variouseasily accessible lesions, such as head and neck cancers, esopha-geal cancers, microinvasive lung cancer, and skin lesions such aspremalignant actinic keratosis.1–4 PDT requires the administra-tion of a photosensitizer that localizes in tumor tissue and isexcited by the appropriate treatment wavelength of light.With the absorption of light, the photosensizer transitionsfrom its ground state to a short-lived excited singlet state.The singlet state photosensitizer transitions to a longer-livedelectronically excited triplet state via intersystem crossing. Intypical type II PDT, which is the focus of this study, the tripletstate transfers energy to molecular ground state oxygen (3O2)that is present in the treatment environment to produce sin-glet-state oxygen (1O2). The production of 1O2 and reactionswith the surrounding biological molecules are thought to bethe major cause of cytotoxicity.5 Due to the high reactivityand short lifetime of 1O2, only cells that are proximal to thearea of 1O2 production are directly affected by PDT.6 Forthat reason, PDT causes significantly less harm to healthy tissuethan chemotherapy or radiation.6,7 A well-defined dosimetricmetric for PDT that is able to predict clinical outcomes thatcan also be implemented in a clinical setting would benefitthe advance of the PDT field.

Benzoporphyrin derivative monoacid ring A (BPD, trade-mark Visudyne®) is a commonly used photosensitizer thatwas approved by the US Food and Drug Administration in2000 for the treatment of wet age-related macular degeneration.8

Utilizing a macroscopic model, reacted singlet oxygen (½1O2�rx)can be calculated to evaluate its effectiveness as a dosimetricpredictor for BPD-mediated PDT outcome. In addition, severalother dose metrics were evaluated in this study, including totallight fluence, photobleaching ratio, and PDT dose, to predict thePDToutcome. Radiation-induced fibrosarcoma (RIF) tumors onmice were treated with BPD-PDT and a range of in-air fluences(30 to 350 J∕cm2) and in-air fluence rates (50 to 150 mW∕cm2).For each PDT treatment group, explicit measurements of BPDconcentration in tumor and tissue optical properties were per-formed pre- and posttreatment. For a subset of mice, real-time in-vivo measurement of BPD concentration and tissue oxy-genation level (½3O2�) throughout PDT were taken to optimizethe photosensitizer-specific PDT photochemical parameters(ξ, σ, and g), reduce their uncertainty from a previous study,and calculate ½1O2�rx. These photochemical parameters wereused to calculate ½1O2�rx for each PDT treatment group. Otherdose metrics, such as photobleaching ratio and PDT dose, weredetermined either directly using explicit measurements pre- andpost-PDT or calculated using the time dependence of BPDconcentration based on the macroscopic model and the defini-tion of PDT dose. This study, to our knowledge, is the first to

*Address all correspondences to: Timothy C. Zhu, E-mail: [email protected] 1083-3668/2017/$25.00 © 2017 SPIE

Journal of Biomedical Optics 028002-1 February 2017 • Vol. 22(2)

Journal of Biomedical Optics 22(2), 028002 (February 2017)


http://dx.doi.org/10.1117/1.JBO.22.2.028002






mailto:[email protected]





investigate the threshold value of ½1O2�rx and the relationshipbetween various dose metrics (fluence, PDT dose, and ½1O2�rx)and the cure index (CI) at 14 days in an in-vivomouse model forBPD-mediated PDT. The results of our study with additionalreal-time measurements of BPD concentration and ½3O2� providereduced uncertainties for the photochemical parameters deter-mined for BPD-mediated PDT, as well as a validation thatour macroscopic model can accurately predict the oxygen con-sumption for BPD-mediated PDT, making it feasible to deter-mine ½1O2�rx without oxygen measurements.

2 Theory and Methods

2.1 Tumor Model

RIF cells were cultured and 30 μl were injected at1 × 107 cells∕ml in the right shoulders of 6 to 8 week old femaleC3H mice (NCI-Frederick, Frederick, Maryland), as describedpreviously.9–12 Animals were under the care of the Universityof Pennsylvania Laboratory Animal Resources. All studieswere approved by the University of Pennsylvania InstitutionalAnimal Care and Use Committee. Tumors were treated whenthey were ∼3 to 5 mm in diameter. The fur of the tumor regionwas clipped prior to cell inoculation, and the treatment area wasdepilated with Nair (Church & Dwight Co., Inc., Ewing, NewJersey) at least 24 h before measurements. Mice were provideda chlorophyll-free (alfalfa-free) rodent diet (Harlan LaboratoriesInc., Indianapolis, Indiana) starting at least 10 days prior to treat-ment to eliminate the fluorescence signal from chlorophyll-break-down products, which have a similar emission range to the BPDfluorescence spectra used to determine the concentration of BPDin the tumor. During the whole treatment, mice were kept underanesthesia on a heat pad at 38°C [see Fig. 1(a)].

2.2 Measurement of Interstitial BenzoporphyrinDerivative Monoacid Ring A Concentration

Fluorescence measurements were made by a custom-mademultifiber spectroscopic contact probe [Fig. 1(b)] describedpreviously13,14 and analyzed using single value decomposition(SVD) fitting.15 Spectra were measured both before and aftertreatment to investigate the effects of and relationship betweenphotobleaching and outcome. An empirical optical property cor-rection factor (CF) is defined as the ratio of SVD between thetissue optical properties of interest (μa, μ 0

s) to the correspondingSVD for a reference tissue optical properties μa ¼ 0.69,μ 0s ¼ 11 cm−1,13,16 with BPD as the photosensitizer and optical

properties measured at 690 nm. A multiplicative CF of the fol-lowing form was used to multiply by raw SVD to obtainSVDcorr:

17

EQ-TARGET;temp:intralink-;e001;63;213CF ¼ C01ð1þ C02μ0sÞ

μ 0s

× exp½ðb1 þ bsμ 0sÞμeff �: (1)

The input optical properties are those measured at 690 nm.The factor was used on raw fluorescence SVD by multiplyingit with CF to get SVDcorr. The values were optimized so thatSVDcorr for phantoms with the same concentration of BPDwere matched [Fig. 2(a)]. Upon optimization, it was found thatC01 ¼ 0.41� 0.16, C02 ¼ 0.142� 0.013, b1 ¼ 0.85� 0.16,and b2 ¼ −0.032� 0.014. In previous publications,13,16 the μ 0

s

dependence in Fig. 2(a) was reversed, and incorrect CF param-eters were provided for the collimated beam geometry and their

respective wavelengths. A separate tissue-simulating phantomwith constant scattering and absorption and varying amountsof BPD were used as a calibration curve to correlate SVDcorr

to actual concentration in μM [Fig. 2(b)]. The line of best-fit[shown as a solid line in Fig. 2(b)] ½BPD� ¼ ð0.0301� 0.0009Þ ×SVDcorr is used to convert SVDcorr to [BPD] in units of μM.Figure 2(c) shows the comparison of in-vivo and ex-vivo mea-surements using methods described previously,13,16 with a solidline of best-fit of the form y ¼ 0.9821x with R2 ¼ 0.9772 toindicate agreement to within 2%. The dashed line representsthe line for y ¼ x. Real-time in-vivo BPD concentration meas-urement over the course of treatment (80 mW∕cm2, 2000 sexposure time) was also determined for a subset of four mice(not included in Table 3) using characteristic fluorescence spec-tra obtained at 30- to 300-s time intervals with excitation at thetreatment light. SVD fitting was used to determine the BPD con-centration. Measured data are shown in Fig. 3(a) with symbols.

2.3 Tissue Oxygen Concentration Measurements

For a subset of four mice (summarized in Table 2) administeredwith BPD (1 mg∕kg), the in-vivo tissue oxygen partial pressurepO2 was measured during PDT treatment using a phosphores-cence-based bare fiber-type 3O2 probe (OxyLite Pro withNX-BF/O/E, Oxford Optronix, Oxford, United Kingdom) foran in-air light fluence rate of 80 mW∕cm2 for 2000 s.Measurements are presented for each 30 s interval during treat-ment. Then, 3O2 concentration was calculated by multiplyingthe measured pO2 with 3O2 solubility in tissue, which is1.295 μM∕mmHg.18,19 Measured ½3O2� was used to refine thephotochemical parameters previously determined20 for the singletoxygen explicit dosimetry model used to calculate ½1O2�rx, andobtained values are summarized in Table 2. Individually mea-sured ½3O2�ðtÞ for each mouse were fit with the model-calculatedvalues. Measured data are shown with symbols and calculated fitsare shown with lines in Fig. 3(b).

Fig. 1 Experimental setup with the (a) multifiber contact spectroscopyprobe and the (b) collimated beam treatment of RIF tumors on mouseshoulder.


Kim, Penjweini, and Zhu: Evaluation of singlet oxygen explicit dosimetry. . .


2.4 Photodynamic Therapy Treatment

An optical fiber with a microlens attachment was coupled with a690-nm diode laser with a maximum output power of 8W (B&WTek Inc., Newark, Delaware) to produce a collimated beam with adiameter of 1 cm on the surface of the tumor [Fig. 1(a)]. Micewere treated with in-air fluence rates (ϕair) of 50 to150 mW∕cm2 and total in-air fluences of 30 to 350 J∕cm2 at690 nm to induce different PDToutcomes and assess the reciproc-ity between BPD concentration and light dose. The “in-air fluencerate” is defined as the calculated irradiance determined by laserpower divided by the treatment area. The “in-air fluence” wascalculated by multiplying the “in-air fluence rate” by the treat-ment time. All mice were injected with 1 mg∕kg BPD throughtail injection at 3 h before the PDT treatment. RIF tumor-bearingmice with (i) no BPD and no light excitation and mice with (ii) noBPD but highest light excitation (ϕair ¼ 150 mW∕cm2 and2333 s exposure) were used as controls (n ¼ 5).

2.5 Tumor Regrowth Rate Analysis

Tumor volumes were tracked daily after PDT. Width (a) andlength (b) were measured with slide calibers, and tumor volumes(V) were calculated using V ¼ π × a2 × b∕6.21 Tumor volumes

Fig. 3 Real-time in-vivo measurement of (a) BPD concentration([BPD]) at the tumor surface and (b) ½3O2� concentration at 3 mmdepth measured for four mice over the course of PDT light delivery(80 mW∕cm2, 160 J∕cm2). The open symbols represent measureddata and the solid curves represent the model-calculated [BPD]and ½3O2� using Eqs. (4) and (5) and the photochemical parameterslisted in Table 2. The black “x” symbols and dashed black line re-present the mean data and fit to data, respectively. The PDT param-eters used to model the mean data are summarized in Table 1.

Fig. 2 Fluorescence optical property correction phantoms and verifica-tion with in-vivo and ex-vivo comparison. (a) Fluorescence SVD ampli-tude for phantom experiments with varying optical properties and thesame BPD concentration (0.25 mg∕kg). The best-fit (shown as dashedlines) uses the form a∕CF, where CF is Eq. (2) and a ¼ 7.645. (Note,CF ¼ 1 is normalized for μa ¼ 0.69, μ 0

s ¼ 11 cm−1.) (b) BPD concentra-tion (in μM) versus the corrected SVD (SVDcorr). The line of best-fit½BPD� ¼ ð0.0301� 0.0009Þ × SVDcorr withR2 ¼ 0.9986 is used to con-vert SVDcorr to [BPD] in μM. (c) The measured in-vivo photosensitizerconcentration using the multifiber contact probe obtained fluorescencespectra versus ex-vivo measured BPD concentration. The line ofbest-fit is of the form y ¼ 0.9821x with R2 ¼ 0.9772. The dashedline in (c) represents the line for y ¼ x .




were tracked for 14 days (Fig. 4), and the tumor regrowth factor(k) was calculated by the best exponential fit [with a formfðdÞ ¼ ekd] to the measured volumes over the days (d). CIwas calculated for each treatment group as

EQ-TARGET;temp:intralink-;e002;63;303CI ¼ 1 −kkctr

; (2)

where k is the tumor regrowth factor for each group and kctr isthe regrowth factor for the control group, which has no injectionof BPD or light illumination.

2.6 Monte-Carlo Simulation of ϕ Distributionin Tumors

The diffusion theory is not valid for the simulation of ϕ in tissuewhen the lateral dimension of the beam geometry becomes com-parable to the mean-free-path of the photons or when the regionof interest is near the air–tissue interface.22 Based on a previousstudy,23 an empirical six-parameter fitting equation was usedto fit the Monte-Carlo (MC) calculated light fluence ratedata22 for a 1-cm diameter field, with μa ¼ 0.52 to 0.80 cm−1

and μ 0s ¼ 7.9 to 14.1 cm−1. The equation is of the following

form:

EQ-TARGET;temp:intralink-;e003;326;328ϕ∕ϕair ¼ INV × ð1 − b × e−λ1dÞðC2e−λ2d þ C3e−λ3dÞ; (3)

where the parameters λ1, λ2, λ3, b, C2, and C3 are functions of μaand μ 0

s and details of each can be found elsewhere.23

INV ¼ ½SSD∕ðSSDþ dÞ�2, where the source-to-surface dis-tance SSD ¼ 9.34 cm based on the measurement of light flu-ence rate in water for the same collimated beam as afunction of depth and fit to the inverse–inverse square law

Table 1 Photochemical parameters for BPD based on Ref. 20. Thestandard deviation for each parameter is based on the fitting of allmice [dashed line in Fig. 3(b)] and is smaller than those in Ref. 20.

Photochemicalparameter Definition Value References

ε (cm−1 μM−1) Photosensitizerextinctioncoefficient

0.0783 20

δ (μM) Low-concentrationcorrection

33 20

β (μM) Oxygen quenchingthresholdconcentration

11.9 20

σ (μM−1) Specificphotobleachingratio

ð1.8� 0.3Þ × 10−5 20

ξ (cm2 mW−1 s−1) Specificoxygenconsumptionrate

ð55� 15Þ × 10−3 20

g (μMs−1) Macroscopicmaximumoxygensupply rate

1.7� 0.4 20

½1O2�rx;sh (mM) Singlet oxygenthresholddose for tumorregrowth

0.99� 0.12 This study

½3O2�0 (μM) Initial oxygenconcentration

40 20

Table 2 PDT parameters (σ, ξ, and g) obtained for four mice treated with in-air fluence of 160 J∕cm2 and in-air fluence rate of ϕair ¼ 80 mW∕cm2

using individual fitting to ½3O2�ðtÞ and ½S0�ðtÞ simultaneously (see Fig. 3). The other photochemical parameters (δ ¼ 33 μM and β ¼ 11.9 μM) arekept the same as in Table 1.

Mouse ½BPD�0 (μM) ξ (cm2 mW−1 s−1) σ (μM−1) g (μMs−1) ½1O2�rxa (mM) ½1O2�rxb (mM)

1 0.76� 0.10 ð60� 8Þ × 10−3 ð1.8� 0.3Þ × 10−3 1.6� 0.4 1.23� 0.24 1.21� 0.40

2 0.87� 0.19 ð60� 10Þ × 10−3 ð1.5� 0.4Þ × 10−3 1.5� 0.4 1.64� 0.31 1.37� 0.17

3 0.58� 0.16 ð50� 10Þ × 10−3 ð1.5� 0.4Þ × 10−3 1.3� 0.3 1.05� 0.33 0.93� 0.13

4 0.80� 0.18 ð50� 7Þ × 10−3 ð1.5� 0.3Þ × 10−3 1.7� 0.3 1.44� 0.28 1.26� 0.21

aCalculated ½1O2�rx using individually fit PDT photochemical parameters and ½3O2�0 ¼ 50 μM.bCalculated ½1O2�rx using the mean PDT photochemical parameters from Table 1.

Fig. 4 Tumor volumes over days after PDT treatment. Solid lines arethe exponential fit to the data with a functional form of ekd , where d isdays after PDT treatment. The resulting tumor regrowth rates, k , andits uncertainty, δk , are listed in Table 3.




formula. The inverse square law factor was added into the MCsimulation results, which is suitable for parallel beams, toaccount for the divergence of the collimated beam from themicrolens. The mean tissue optical properties are found to beμ̄a ¼ 0.69� 0.12 cm−1 and μ̄ 0

s ¼ 11� 3 cm−1 for RIF tumorsat 690 nm, and the maximum error for using the mean opticalproperties is �15% (data not shown).

2.7 Macroscopic Singlet Oxygen Modeling

The typical type II PDT process can be described by a set ofkinetic equations, which can be simplified to describe the cre-ation of ½1O2�rx.18,20 These equations are dependent on the tem-poral and spatial distribution of light fluence, photosensitizerconcentration (½S0�), ground state oxygen concentration(½3O2�), and the photosensitizer-specific reaction-rate parame-ters. The relevant equations are

EQ-TARGET;temp:intralink-;e004;63;142

d½S0�dt

¼ −½3O2�

½3O2� þ βξσð½S0� þ δÞϕ½S0�; (4)


d½3O2�dt

¼ −½3O2�

½3O2� þ βξϕ½S0� þ g

�1 −

½3O2�½3O2�ðt ¼ 0Þ

�; (5)


d½1O2�rxdt

¼ ½3O2�½3O2� þ β

ξϕ½S0�; (6)

where g is the maximum oxygen supply rate to tissue, δ is thelow-concentration correction, β is the oxygen quenching thresh-old concentration, σ is the specific photobleaching ratio, and ξ isthe macroscopic maximum oxygen supply rate. The value ofeach of these parameters was found by fitting the measured½3O2� to the calculated values; they are summarized in Table 1.If the parameters are 10% over- or underestimated, calculated½1O2�rx will deviate up to 12%. An increased σ estimates asmaller ½1O2�rx while an increased g or ξ estimates larger ½1O2�rx.

Figure 5 is a flowchart showing how ½1O2�rx is calculated.The depth dependence of ϕ is calculated using an analyticalfit of MC simulation, Eq. (3), and published fitting parameters.23

For each spatial location, ½S0�ðtÞ and ½3O2�ðtÞ can be calculatedby solving the coupled differential equations [Eqs. (4) and (5)]using the initial conditions for ½S0�0 based on fluorescence meas-urement before PDT and its assumed spatial homogeneous, theinitial ½3O2�0 value (e.g., 50 μM from Tables 1), and ϕðdÞ. Thelight fluence rate does not change with time. Finally, ½1O2�rx iscalculated using Eq. (6).

Table 3 In-air light fluence, in-air light fluence rate, ϕair, photosensitizer concentrations pre- and post-PDT, [BPD]pre and [BPD]post, PDT dose at3 mm depth, reacted singlet oxygen concentration, ½1O2�rx, at 3 mm depth, tumor regrowth rate, k , and CI, for each PDT treatment group. Number ofmice per group is shown in the second column. The same index for each PDT treatment group is used for Figs. 4 and 7.

Index#

mice

In-airfluence(J∕cm2)

ϕair(mW∕cm2)

Time(s)a

½BPD�pre(μM)

½BPD�post(μM)

PDTdoseb

(μMJ∕cm2)½1O2�rxc(μM)

k(1/days)

Cureindex,

CI ¼ 1 − k∕kctr

1 5 30 50 600 0.53� 0.24 0.33� 0.14 14.1� 6.0 0.39� 0.15 0.40� 0.03 0.0337� 0.02

2 5 75 400 0.72� 0.22 0.32� 0.12 19.2� 6.0 0.45� 0.05 0.38� 0.03 0.0556� 0.03

3 5 150 200 0.56� 0.29 0.27� 0.09 15.2� 7.9 0.29� 0.05 0.40� 0.03 0.0237� 0.02

4 3 70d 50 1400 0.73� 0.21 0.07� 0.09 39.6� 8.1 0.90� 0.21 0.28� 0.02 0.3151� 0.08

5 3 100d 75 1333 0.41� 0.09 0.05� 0.03 28.7� 5.9 0.60� 0.20 0.37� 0.05 0.1037� 0.05

6 3 135d 50 2700 0.50� 0.18 0.04� 0.02 41.0� 8.4 0.78� 0.18 0.34� 0.08 0.1646� 0.04

7 5 75 1800 0.53� 0.21 0.05� 0.02 44.2� 10.9 0.82� 0.28 0.32� 0.02 0.2139� 0.07

8 5 150 900 0.58� 0.12 0.07� 0.02 50.2� 18.8 0.85� 0.31 0.28� 0.08 0.3240� 0.10

9 3 150d 75 2000 0.84� 0.27 0.10� 0.02 75.4� 17.9 1.30� 0.42 0 1� 0.08

10 5 100 1500 0.66� 0.24 0.07� 0.02 59.9� 12.2 1.03� 0.37 0.11� 0.02 0.7432� 0.08

11 3 250d 75 3333 0.58� 0.19 0.02� 0.02 64.0� 14.7 0.96� 0.26 0.25� 0.01 0.3878� 0.07

12 5 150 1667 0.77� 0.20 0.01� 0.02 93.0� 17.8 1.26� 0.29 0 1

13 5 300 150 2000 0.77� 0.26 0 97.9� 28.2 1.27� 0.24 0 1

14 5 350 150 2333 0.81� 0.34 0.04� 0.05 108.3� 20.8 1.35� 0.30 0 1

15 5 Control 0 0 0 0 0 0 0.41� 0.05 0

aTotal treatment time.bPDT dose is defined as the time integral of the product of the photosensitizer concentration and the light fluence rate (ϕ), ½S0�ðtÞ is calculated usingthe parameters in Table 1.

c½1O2�rx is calculated using Eqs. (4)–(6) using the parameters listed in Table 1.dOptical properties were measured in one mouse per group.




For a subset of four mice, ½S0� and ½3O2� concentration overtime during the course of PDT delivery were measured. ½S0� wasdetermined by collecting the characteristic fluorescence spectraof BPD due to excitation by the treatment light. To minimize thepossible effect of optical properties change at 405 nm on fluo-rescence SVDcorr, which is not included in Eq. (1), we used ex-vivo measurement of ½S0� to validate our in-vivo fluorescencemethod in the same mouse population [Fig. 2(c)]. ½3O2� wasmeasured using the phosophorescence-based oxygen probementioned in Sec. 2.3. These quantities over time were fitwith Eqs. (4) and (5) to validate the parameters of ξ, σ, andg obtained previously.20 The objective function minimizedduring the fitting routine was the root-mean-square error(RMSE) between model-calculated ½3O2� and measured ½3O2�(RMSE ¼ ðj½3O2�measured − ½3O2�calculated2Þ1∕2). Minimizationof the objective function was performed using the function“fminsearch” in MATLAB®.

All fitting and simulation were performed using MATLAB®

R2014b (Natick, Massachusetts) on an iMac OSX version10.10.5 (processor 2.9 GHz Intel Core i5, 16 GB memory).The calculation times were in seconds for the spatially coupleddifferential equations. A more detailed description of the macro-scopic model has been published previously.9,18,20,24

3 ResultsBPD-mediated PDTwith different in-air fluences, different ϕair,and different exposure times was performed in mouse modelsbearing RIF tumors. Tissue optical properties, photosensitizerconcentration, and tissue oxygenation were measured to calcu-late photobleaching percentage, PDT dose, and ½1O2�rx. Table 3summarizes all of the treatment conditions, as well as the mea-sured and calculated quantities using the photochemical param-eters summarized in Table 1.

Four mice, summarized in Table 2, were used to monitor thephotosensitizer concentration and ½3O2� throughout the treatmentusing ϕair ¼ 80 mW∕cm2 and total fluence of 160 J∕cm2. Themeasured results (open symbols) were compared to calculatedvalues (solid lines) in Fig. 3 to validate the photochemical param-eters used in the calculation of ½1O2�rx. R2 values are provided toevaluate their fits. Calculations were performed using Eqs. (4)–(6)

and the photochemical parameters found from individual fits of½3O2�ðtÞ summarized in Table 2, as well as the photochemicalparameters for the mean data summarized in Table 1 and mea-sured values of initial photosensitizer concentration.

Measured tumor volume over 14 days after treatment foreach treatment group is shown in Fig. 4. Compared to controlmice, all treatment conditions had significant control of thetumor regrowth after PDT. CI was calculated for each treatmentgroup using Eq. (2). PDT using 150 J∕cm2 with 75 mW∕cm2

was a more effective treatment than with 100 mW∕cm2. Eachtumor volume was normalized to the mean initial volume, sothey are equal on day 0 (treatment date) before fitting for thetumor regrowth rate.

BPD concentration ([BPD]) was measured both before andafter PDT treatment. Measured [BPD] was compared to model-calculated values for all of the treatment conditions and is shownin Fig. 6(a). The symbols represent the measured values, and thesolid lines are model-calculated photosensitizer concentrationduring treatment. Figure 6(b) shows the spatial distribution ofreacted singlet oxygen in the RIF tumor model. The symbolsindicate ½1O2�rx at 3 mm tumor depth for each treatment condi-tion. The depth of 3 mm was chosen as it encompasses the initialtumor size of all treated tumors. Previous publications also cal-culated ½1O2�rx at 3 mm, and results of this study can be com-pared to those directly.

Several dose metrics were evaluated for predicting the treatmentoutcome. Figure 7 shows the correlation of CI (tumor control) ver-sus in-air fluence, photobleaching ratio (%), PDT dose at 3 mmdepth, and ½1O2�rx at 3 mm depth. The mean of k and kctr forall mice in each treatment group (number of mice per groupis shown in Table 3) was used to determine CI using Eq. (1).Photobleaching was determined by the ratio of BPD SVDcorr mea-sured immediately following treatment (½SVDcorr�post) to the BPDconcentration measured prior to treatment (½SVDcorr�pre) and calcu-lating 1 − ð½SVDcorr�postÞ∕ð½SVDcorr�preÞ. PDT dose is defined bythe time integral of the product of the ϕ at a 3-mm tumor depthand the local BPD concentration. Figures 7(a)–7(d) show thecorrelation of CI to fluence, photobleaching percentage, PDTdose, and mean ½1O2�rx along with their line of best-fit. The linesof best-fit (shown with solid lines) are CI ¼ ð3.309 × 10−3Þx,

Fig. 5 Flowchart for the calculation of ½1O2�rx based on initial conditions of ½S0�0 and ϕðdÞ. The initialoxygen concentration ½3O2�0 is chosen to be 40 μM for most of the data analysis except for the individualfits for Fig. 3, where ½3O2�0 ¼ 50 μM.




CI¼ð1.118×10−3Þe0.06731x, CI¼1.052∕ð1þ1014.4e−0.08172xÞ,and CI¼1.08∕ð1þ3490e−8.301xÞ with R2¼0.6260, 0.6274,0.9360, and 0.9850 for fluence, photobleaching percentage,PDT dose, and ½1O2�rx at 3 mm, respectively.

4 DiscussionsAs shown in Fig. 3, the photochemical parameters σ, ξ, and gwere validated by measuring [BPD] changes and ½3O2� duringthe PDT treatment for individual mice and applying the param-eters to the explicit dosimetry model. Based on a previousstudy, the parameters of σ, ξ, and g were found to beð1.8� 0.3Þ × 10−5 μM−1, ð55� 15Þ × 10−3 cm2 mW−1 s−1,and 1.7� 0.4 μM−1, respectively.20 The standard deviation ofeach parameter is reduced based on the fitting of ½S0� and½3O2� as shown in Fig. 3, which is a more robust data set forderiving the photochemical parameters. Each individually mea-sured ½3O2� in Fig. 3 was fitted to validate the photochemicalparameters as shown in Table 2. RMSE between measuredand calculated values of ½3O2� was used as a measure ofgood fit.

To assess the effect of photochemical parameters, the valuesof calculated reacted singlet oxygen concentration, ½1O2�rx,

using the individually obtained photochemical parameters foreach mouse (from Table 2) were compared to ½1O2�rx calculatedusing the photochemical parameters from a previous study,20

from Table 1. For the same mouse, ½1O2�rx calculated usingthe two sets of photochemical parameters agree with eachother to within a maximum uncertainty of 20% and a standarddeviation of 8% (see Table 2). The good agreement betweenmeasurement and calculation of photosensitizer concentrationand oxygen concentration (Fig. 3) provided a validation ofthe photochemical parameters determined previously andallowed for reduction in the uncertainty of each parameter.For BPD, the comparisons between the measured ½3O2� and cal-culation for a subset of four mice (Fig. 3b) show that our macro-scopic model can accurately predict ½3O2� for the mice studiedwith R2 values 0.70 to 0.90. The agreement between measuredand calculated ½3O2� makes it unnecessary to measure the oxy-gen concentration directly during PDT. One complication of thecomparison between measurement and calculation for in-vivooxygen concentration is the uncertainty of the depth at whichoxygen concentration was measured, which lies at around3 mm. To illustrate this effect, the spatial and temporal variationsof ½3O2� were shown for various ϕair (20, 50, 75, and150 mW∕cm2): Figs. 8(a)–8(c) show the temporal changes of½3O2� at 1, 3, and 5 mm with ½BPD� ¼ 0.57 μM (the mean valueof BPD concentration for all mice studied); Figs. 8(d)–8(f)show the temporal changes of ½3O2� at 1, 3, and 5 mm with½BPD� ¼ 0.87 μM. Initial ½3O2� of 40 μM and the photochemi-cal parameters in Table 1 were used for the calculations. As thedepth increases from 1 to 5 mm, the minimum value of ½3O2�increases, while the rate of ½3O2� recovery due to photobleaching(for 50 to 2000 s) decreases. Higher initial [BPD] will cause alarger drop of ½3O2�, depending on the light fluence rate. Lowerlight fluence rates will have less ½3O2� consumption during PDT.The optimized depth for the best agreement between model andmeasurement is found to be 3 mm, corresponding to the place-ment of the oxygen probe during PDT.

Compared to control mice, all treated mice with total fluen-ces larger than 30 J∕cm2 had significant control of the tumorregrowth after PDT (see Fig. 4). However, mice with tumors ofabout the same size, administered the same BPD dose, andtreated with identical fluence exhibited different survival andtumor control as ϕair was changed. In the group of mice treatedto 150 J∕cm2, CI increased as the source strength was loweredfrom 100 to 75 mW∕cm2. This is in agreement with priorreports of increased therapeutic response with a reduced ϕair

by expanding the radius of 1O2 formation around a tumor capil-lary in a multicell tumor spheroid model.25

Figure 6(a) compares the measured pre- and post-PDT BPDconcentration, [BPD], versus calculated [BPD] during treatmentfor each treatment condition using the photochemical parame-ters summarized in Table 1. The good agreement [for mean ½S0�,R2 ¼ 0.88 in Fig. 6(a)] between the measured [BPD] pre- andpost-PDT further validates the photochemical parameters(Table 1) used for the modeling. Figure 6(b) shows the spatialdistribution of ½1O2�rx for each treatment condition. The value of½1O2�rx at 3 mm is shown with symbols. While the comparisonof CI versus ½1O2�rx was done using ½1O2�rx at 3 mm, the value of½1O2�rx is almost a constant for depths between 1 and 4 mm formost of the PDT treatment groups, indicating that the correlationbetween ½1O2�rx and CI in Fig. 7(c) should be equally valid forany depth between 1 and 4 mm.

Fig. 6 (a) The temporal changes of BPD concentration versus fluenceat 3 mm depth for the treatment conditions. The solid lines representthe calculated changes of photosensitizer concentration during treat-ment. The symbols show the measured BPD concentration pre- andpost-PDT. Initial drug concentrations for the calculation were matchedto measured values. (b) The spatial distribution of reactive singlet oxy-gen (½1O2�rx) in the RIF tumors calculated for different treatment con-ditions. ½1O2�rx at 3 mm tumor depth is shown as symbols. R2 valuesfor each calculation are shown in the legend.




Fluence, photosensitizer photobleaching ratio, PDT dose,and ½1O2�rx at 3 mm were compared as dosimetric quantitiesto estimate the outcome of BPD-mediated PDT for RIF tumorson a mouse model. The outcome was evaluated by the calcula-tion of CI. No tumor regrowth up to 14 days after treatmentresulted in a CI of 1. The goodness of the fit and the correspond-ing upper and lower bounds of the fits (gray area) to the fluence,BPD photobleaching, PDT dose, and mean ½1O2�rx are presentedin Fig. 7. Figure 7(a) shows that, while fluence correlates lin-early with the PDT outcome, it exhibits large uncertainties asdefined by the large bounds of the gray area, as well as bythe low value of R2 ¼ 0.67. As evident by the lower value ofR2 ¼ 0.63 and a relatively large bound of gray area in Fig. 7(b),the BPD photobleaching ratio is not a better dosimetricquantity for predicting the PDT outcome as compared tofluence. The BPD concentration (∼0.2 to 0.8 μM) as used clin-ically is much lower than the value of δ (¼33 μM), and this maybe a reason for the poor correlation of the photobleaching ratioand CI. In photobleaching-based implicit dosimetry, a muchmore sophisticated model than simple bleaching fraction isused, and the result of this study does not mean that other meth-odologies of photobleaching-based implicit dosimetry will notbe applicable for PDT dosimetry. As shown in Fig. 7(c),PDT dose allows for reduced subject variation and improvedpredictive efficacy as compared to fluence and photobleaching.

PDT dose showed a better correlation with CI with a highervalue of R2 ¼ 0.97 and a narrower band of gray area as itaccounts for both light dose and tissue [BPD] levels. How-ever, PDT dose overestimates ½1O2�rx in the presence ofhypoxia as it does not account for the oxygen dependence of1O2 quantum yield. The goodness of fit R2 ¼ 0.99 and the nar-rowest gray area in Fig. 7(d) shows that the mean ½1O2�rx cor-relates the best with CI. ½1O2�rx accounts for the key quantities oflight fluence, photosensitizer concentration, and tissue oxy-gen level.

Based on the findings of this study, PDT dose and ½1O2�rxexhibit threshold dose behavior as they can be fitted by asigmoid function SðxÞ ¼ 1∕f1þ e½−ðx − x0Þ∕w0�g, wherex0 ¼ 58 μMJ∕cm2 with uncertainty w0 ¼ 12 μMJ∕cm2 andx0 ¼ 0.98 mM with uncertainty w0 ¼ 0.12 for PDT dose and½1O2�rx, respectively. For PDT dose, x0 can be converted tothe absorbed dose by BPD by multiplying by the extinctioncoefficient (ε ¼ 0.0783 μM−1 cm−1), resulting in 4.5 J∕cm3,which corresponds to ð16� 4Þ × 1018 photons∕cm3 (by divid-ing the energy per photon hc∕λ ¼ 2.88 × 10−19 J for λ ¼690 nm). The PDT dose threshold for BPD is in agreementwith those reported for 2-(1-hexyloxyethyl)-2-devinyl pyro-pheophorbide-a (HPPH) (19 × 1018 photons∕cm3)16 and ourpreliminary results for BPD (13.4 × 1018).26 The mean ½1O2�rxthreshold concentration of x0 ¼ 0.98� 0.12 mM is similar to

Fig. 7 CI plotted against (a) fluence at a 3 mm tumor depth, (b) measured photosensitizer photobleach-ing (%), (c) calculated PDT dose at 3 mm depth, and (d) mean reacted singlet oxygen at 3 mm depth(½1O2�rx) calculated using Eqs. (4)–(6) and the parameters summarized in Table 1. The solid lines showthe best-fit to the data with functional forms CI ¼ ð3.309 × 10−3Þx , CI ¼ ð1.118 × 10−3Þe0.06731x ,CI ¼ 1.052∕ð1þ 1014.4e−0.08172x Þ, and CI ¼ 1.08∕ð1þ 3490e−8.301x Þ with R2 ¼ 0.6260, 0.6274,0.9360, and 0.9850 for (a), (b), (c), and (d), respectively. The gray region indicates the upper andlower bounds of the fit with 95% confidence level.




those published for HPPH (1.00 mM)16 and the published pre-liminary result for BPD (0.82 mM).26 The increases for bothPDT dose and ½1O2�rx threshold dose for BPD are due to an11% increase of BPD drug concentration after a more compre-hensive analysis of the fluorescence CF for mice revealed an11% error in the original calibration curve for BPD concentra-tion [Fig. 2(b)]. We want to point out that the definition of thevalue of the threshold doses for both PDT dose and ½1O2�rx is thevalue when CI ¼ 0.5 rather than when CI ¼ 1 (see Fig. 7). Boththe current and previously published results26 use the samephotochemical parameters (Table 1).

5 ConclusionThe response of mouse RIF tumors to PDT depends on the tis-sue oxygenation, photosensitizer uptake, total energy delivered,and the ϕ at which the treatment is delivered. An accuratedosimetry quantity for the evaluation of the treatment outcomeshould account for all of these parameters. This study evaluatedthe efficacy and outcomes of different PDT treatments and howfluence, BPD photobleaching, PDT dose, and ½1O2�rx compareas dosimetric quantities. The correlation between CI and ½1O2�rxsuggests that ½1O2�rx at 3 mm is the best quantity to predict the

Fig. 8 Temporal dependence of ½3O2�ðtÞ calculated for various in-air fluence rates (20, 50, 75, and150 mW∕cm2) at depths of 1, 3, and 5 mm in the tumor for two initial BPD concentrations, [BPD]:(a)–(c) 0.57 μM and(d)–(f) 0.87 μM. Photochemical parameters in Table 1 are used for ½3O2� calculationusing Eqs. (4) and (5).




treatment outcome for a clinically relevant tumor regrowth end-point. PDT dose is the second most effective dosimetry quantitywhen compared to fluence or photosensitizer photobleachingbut is worse than ½1O2�rx as it does not account for the consump-tion of ½3O2� for different ϕ. For BPD in RIF tumors, our mea-surements show consistent temporal dependence of in-vivooxygen concentration during PDT that can be well modeledby our macroscopic model (for mean ½3O2�, R2 ¼ 0.70), imply-ing that it is not necessary to make ½3O2� measurements duringPDT to obtain ½1O2�rx, as well as by using our model. This studyvalidated the model and photochemical parameters for BPD-mediated PDT for an endpoint that is clinically relevant.

DisclosuresNone of the authors have a financial conflict of interest in thiswork.

AcknowledgmentsThe authors would like to thank Dr. Jarod C. Finlay, DaytonMcMillan, and Dr. Baochang Liu for useful discussions andexperimental support and Dr. Theresa Busch for her advice con-cerning the mouse studies and protocols. We thank Dr. CostasKoumenis and the Department of Radiation Oncology ResearchDivision, University of Pennsylvania for providing the OxfordOxylite instrument for oxygen measurements. This work wassupported by grants from the National Institutes of HealthNos. R01 CA154562 and P01 CA87971.

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Michele M. Kim received her BA and MS degrees in physics from theUniversity of Pennsylvania in 2012 and is currently a PhD candidate atthe University of Pennsylvania in physics while pursuing a certificatein medical physics. Her research interests include preclinical and clini-cal photodynamic therapy dosimetry.

Rozhin Penjweini received her PhD in 2012 in physics fromthe University of Vienna. She is currently a postdoctoral researcherin the Department of Radiation Oncology at the University ofPennsylvania. Her current research interest is in vivo explicit photo-dynamic therapy (PDT) and singlet oxygen dosimetry. She also haspractical experience in various fluorescence microscopy techniquesfor studying the structure, transport, and stability of nanomedicinesfor PDT treatment of cancer.

Timothy C. Zhu received his PhD in 1991 in physics from BrownUniversity. He is currently a professor in the department of radiationoncology at the University of Pennsylvania. His current research inter-ests include explicit PDT dosimetry, singlet oxygen explicit dosimetry(SOED), integrated system for interstitial and intracavitory PDT,diffuse optical tomography, in vivo dosimetry, and external beam radi-ation transport.




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Evaluation of singlet oxygen explicit dosimetry for predicting ... · Keywords: photodynamic therapy; singlet oxygen explicit dosimetry, explicit dosimetry; singlet oxygen; photodynamic